[Ch3] Rational multiples of pi for 3-17

[pingpingy1]

What is the content you want to add? What problem is it the solution to?
In problem 3-17, $a$ could be a rational multiple of $\pi$, in which case the poles of the integrand are modified.
The solution must be expanded such that these cases be addressed.

Additional context

[pingpingy1]

It seems likely on first glance that only the residue calculation need be modified; the contour integral logic seems to be identically applicable to these cases.

If $a = \pi \frac{p}{q}$ where $p$ and $q$ are coprime, then precisely the poles at $qm\pi$ $(m \text{ integer})$ are removed, and we only need to subtract the poles at these points (verify!).